CTET Mathematics Paper 2 MCQs with Answers Set 03

Multiple Choice Questions (MCQs) for CTET : Mathematics

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These 29 CTET Mathematics Paper 2 multiple choice questions cover mathematics content and pedagogy of mathematics. Each question has the correct answer with a step-by-step explanation and a short teacher's note, so you can practise for the Central Teacher Eligibility Test and check your understanding.

Multiple Choice Questions

Question 1: It has been observed that people involved in occupations that require mathematical skills of computation and estimation like vendors, construction workers etc. are often not able to cope up with formal school mathematics. Which of the following offers the most appropriate explanation for this?
(a) School mathematics requires a different level of intelligence
(b) Many people are inherently incapable of learning school mathematics
(c) School curriculum usually does not incorporate ways of teaching-learning specific to learners' cultural context
(d) People coming from these occupational backgrounds do not have time to practice problems given in the textbook at home
Show Answer & Explanation

Answer: (c) School curriculum usually does not incorporate ways of teaching-learning specific to learners' cultural context

Explanation:
1. These people use mathematics well in their work, so ability is not the issue.
2. The school curriculum often ignores the learners' cultural context and informal methods.

Teacher's Note:
1. Informal everyday mathematics should be linked with school mathematics.
2. Deficit explanations about ability are wrong.

Question 2: A student in class VI gives the following statement in a mathematics class: "A 3D shape can be transformed into a 2D shape". Which of the following concepts is the child correctly applying to the above situation?
(a) Viewing objects from different sides.
(b) Scaling
(c) Rotation
(d) Symmetry
Show Answer & Explanation

Answer: (a) Viewing objects from different sides.

Explanation:
1. A 3D solid viewed from the front, top or side gives a 2D picture.
2. So the idea used is viewing objects from different sides.

Teacher's Note:
1. Views and nets are common 3D to 2D links in Class VI.
2. Scaling, rotation and symmetry do not change dimension.

Question 3: After the completion of unit on algebra, a teacher decides to develop a rubric for assessing the learners on problem solving and reasoning skills. Which of the following rubric statements are most appropriate to be included in the rubric?
(a) Understands the problem before solving it.
(b) Checks the answers from answer key and develops strategies accordingly.
(c) Constructs logical progression of mathematical statements.
(d) Explains ideas only in writing using words, pictures and numbers.
Choose the correct options:
(a) Only (d)
(b) (b) and (c)
(c) (a) and (c)
(d) (b) and (d)
Show Answer & Explanation

Answer: (c) (a) and (c)

Explanation:
1. Understanding the problem (a) and building logical steps (c) are core problem-solving and reasoning skills.
2. Looking at an answer key (b) is not a skill, and 'only in writing' (d) restricts communication.

Teacher's Note:
1. Rubrics describe skills, not shortcuts.
2. Communication can also be oral.

Question 4: According to National Curriculum Framework (2005), major aim of mathematics education in schools is to:
(a) Analyse the child's thought process
(b) Mathematize the child's thought process
(c) De-mathematize the child's thought process
(d) Develop the problem-solving ability in learner
Show Answer & Explanation

Answer: (b) Mathematize the child's thought process

Explanation:
1. NCF 2005 position paper says the main goal of mathematics education is to mathematise the child's thinking.
2. Problem solving is a means, not the stated main goal.

Teacher's Note:
1. Mathematisation includes reasoning, abstraction and problem solving.
2. Remember 'mathematise' as the key NCF word.

Question 5: Which of the following cannot be considered as one of the reasons of mathematics anxiety in students?
(a) Low achievement in mathematics examination
(b) Teaching-learning experiences in classroom
(c) Abstract nature of mathematics
(d) Gender differences
Show Answer & Explanation

Answer: (d) Gender differences

Explanation:
1. Poor results, classroom experiences and abstraction can all cause anxiety.
2. Gender in itself is not a cause; differences arise from stereotypes, not gender.

Teacher's Note:
1. Avoid assuming innate gender differences.
2. Causes are environmental and pedagogical.

Question 6: A teacher presents the real-life problem in the classroom that in a village where almost all the villagers / households are from economically weaker section only three are affluent households. For providing the maximum benefits of govt scheme to villagers, a survey is being done. In this situation, which one of the following measures of central tendency will be appropriate to find out the average income of that village?
(a) Mean
(b) Median
(c) Mode
(d) Harmonic Mean
Show Answer & Explanation

Answer: (b) Median

Explanation:
1. Three very high incomes (outliers) would raise the mean and misrepresent the typical household.
2. The median is unaffected by extreme values and so is appropriate.

Teacher's Note:
1. Use median when data has outliers.
2. The mode would also be near typical but the median is the standard choice.

Question 7: For assessing the performance of students in mathematics over a period of time, Mr. Raju has collected exemplary works of his class VIII students which includes assignments, project reports, homework, models, unit tests and class tests etc. The assessment strategy used by Mr. Raju is a
(a) Cumulative reward.
(b) Anecdotal reward.
(c) Portfolio.
(d) Rubrics.
Show Answer & Explanation

Answer: (c) Portfolio.

Explanation:
1. A portfolio is a purposeful collection of a student's work over time.
2. Rubrics are scoring guides and the other two terms are not assessment strategies.

Teacher's Note:
1. Portfolios show growth over time.
2. Rubrics score work against criteria.

Question 8: A teacher folds a square sheet of paper into half and punches a hole in the folded sheet of paper. She then unfolds the paper. Which of the following topics she can teach with this activity?
(a) Symmetry and volume
(b) Volume and fraction
(c) Symmetry and fraction
(d) Surface area of a square
Show Answer & Explanation

Answer: (c) Symmetry and fraction

Explanation:
1. The two holes are mirror images about the fold, which shows symmetry.
2. Folding into half also shows the fraction one half.

Teacher's Note:
1. Paper folding is a classic symmetry activity.
2. A paper has area, not volume, in this activity.

Question 9: Which of the following is NOT an advantage of 'Analytical rubrics'?
(a) It gives diagnostic information to teacher
(b) It gives formative feedback to students
(c) It is good tool for summative assessment
(d) It is easier to link to instructions than to holistic rubrics.
Show Answer & Explanation

Answer: (c) It is good tool for summative assessment

Explanation:
1. Analytical rubrics score each criterion separately, giving diagnostic and formative information and a link to instruction.
2. Holistic rubrics, not analytical ones, are the quick tool for summative grading.

Teacher's Note:
1. Analytical: detailed feedback; holistic: overall judgment.
2. Detail makes analytical rubrics time-consuming for summative use.

Question 10: Which of the following tasks is least likely to develop critical thinking in mathematics among students?
(a) Evaluate 72 × 63 in three different ways and compare the results.
(b) Formulate any two situations to represent the equation 7x + 3 = 24.
(c) A student calculated the volume of a right circular cylinder of radius 3.5 cm and height 10 cm as 38.5 cm. Where did she go wrong?
(d) Calculate the volume of a right circular cylinder of radius 3.5 cm and height 10 cm.
Show Answer & Explanation

Answer: (d) Calculate the volume of a right circular cylinder of radius 3.5 cm and height 10 cm.

Explanation:
1. Options a, b and c ask for comparison, problem posing and error analysis, which develop critical thinking.
2. Option d is a single routine calculation using a formula.

Teacher's Note:
1. Error analysis (volume 385 cm³, units wrong) is higher order.
2. Routine computation is lower order.

Question 11: Which of the following is the most appropriate way to teach the middle school students that mathematical probability of any outcome in a random event lies between 0 to 1?
(a) By writing the formula of probability as possible outcomes divided by total number
(b) By using videos based on solving problems on probability from internet
(c) By telling the students to do some experiments and verify of outcomes
(d) By conducting a practical experiment of any random event like throwing a dice, flipping a coin etc. and asking students to note the outcomes
Show Answer & Explanation

Answer: (d) By conducting a practical experiment of any random event like throwing a dice, flipping a coin etc. and asking students to note the outcomes

Explanation:
1. Students should do a concrete experiment and record outcomes themselves.
2. Frequencies of outcomes then show that each relative frequency lies between 0 and 1.

Teacher's Note:
1. Option c is vague; d names the experiment and recording.
2. Hands-on first, formula later.

Question 12: At primary level, children's thinking in mathematics progresses from:
(A) abstract to concrete
(B) complex to simple
(C) simple to complex
(D) concrete to abstract
Choose the correct option:
(a) (A) and (B)
(b) (B) and (C)
(c) (A) and (D)
(d) (C) and (D)
Show Answer & Explanation

Answer: (d) (C) and (D)

Explanation:
1. Children's thinking develops from concrete to abstract and from simple to complex ideas.

Teacher's Note:
1. Piaget: concrete operations come before abstract reasoning.
2. Sequence topics from simple to complex.

Question 13: Which among the following is an open ended question?
(a) Identify three objects which are in the shape of a cuboid
(b) If sum of two numbers is 13 and their difference is 3, what are the numbers?
(c) Write as many as possible even prime numbers
(d) Write even numbers, between 10 and 20 which are multiples of 2 and 3
Show Answer & Explanation

Answer: (a) Identify three objects which are in the shape of a cuboid

Explanation:
1. Option a has many correct answers (a box, a brick, a matchbox).
2. The others have a single answer: 8 and 5; only 2 is even and prime; 12 and 18.

Teacher's Note:
1. Open-ended: many correct answers.
2. Check whether the answer set is unique.

Question 14: Which of the following is NOT true about a mathematical theorem?
(a) They are generalized statements of truth about certain mathematical facts.
(b) They can be proved mathematically.
(c) There is only one way to prove any theorem.
(d) Unproved theorems are called conjectures.
Show Answer & Explanation

Answer: (c) There is only one way to prove any theorem.

Explanation:
1. A theorem is a general statement that has been proved.
2. Many theorems have several different proofs (the Pythagoras theorem has hundreds).

Teacher's Note:
1. Multiple proofs are possible.
2. Unproved statements are conjectures.

Question 15: Which of the following is considered to be the most effective ways to enhance student's interest in mathematics beyond school hours?
(a) Forming mathematics clubs which involves various activities related to mathematics learning for students
(b) Telling students to participate in various competitive exams
(c) Giving a lot of home work involving mathematics questions
(d) Providing the students with a lot of teaching learning materials like textbooks, sample papers etc.
Show Answer & Explanation

Answer: (a) Forming mathematics clubs which involves various activities related to mathematics learning for students

Explanation:
1. Clubs offer enjoyable, collaborative activities that raise interest.
2. Exams, homework load and sample papers add pressure.

Teacher's Note:
1. Interest grows through enjoyable activities.
2. Avoid pressure-based options.

Question 16: According to National Curriculum Framework 2005, the goal of mathematics teaching in school curriculum is that children learn "Important Mathematics". Important Mathematics implies:
(a) Important formulae in mathematics must be focused upon
(b) Algorithms in mathematics form an important part hence should be included as a part of important mathematics
(c) Mathematics must include such meaningful problems, which teacher and students consider worth solving and as part of their daily lives
(d) Those concepts and topics should be considered important in mathematics that turn out employable adults for social and economic development
Show Answer & Explanation

Answer: (c) Mathematics must include such meaningful problems, which teacher and students consider worth solving and as part of their daily lives

Explanation:
1. NCF 2005 defines important mathematics as meaningful problems that teachers and students consider worth solving and that relate to daily life.
2. Formulae, algorithms and employability are not the definition.

Teacher's Note:
1. Meaning and relevance define importance.
2. Pick the answer closest to NCF wording.

Question 17: Which of the following can be the best explanation of children developing a fear of mathematics?
(a) Children fear mathematics if their IQ is low
(b) Since mathematics is an abstract discipline, it is natural for children to have difficulties in understanding and therefore all students will develop a fear of it
(c) It is the most objective form of knowledge that requires rigour, failing which children develop an aversion for the subject
(d) Teachers play a significant role in invoking interest about mathematics in children, and conversely they may also contribute to the fear by penalizing students for committing errors
Show Answer & Explanation

Answer: (d) Teachers play a significant role in invoking interest about mathematics in children, and conversely they may also contribute to the fear by penalizing students for committing errors

Explanation:
1. Fear of mathematics is mostly learned from the classroom environment.
2. Teachers can spark interest or create fear by penalising errors.

Teacher's Note:
1. Anxiety is caused by teaching and assessment practices, not ability.
2. Reject statements that blame low IQ or say all students will fear it.

Question 18: A mathematics teacher records classroom observation either during or after the lesson by writing short notes in a brief narrative style. It is an example of maintaining:
(a) Rubrics
(b) Anecdotal Records
(c) Checklist
(d) Portfolio
Show Answer & Explanation

Answer: (b) Anecdotal Records

Explanation:
1. Short narrative notes about a child's behaviour or learning, written during or after an event, are anecdotal records.
2. Rubrics and checklists use fixed criteria, and a portfolio is a collection of work.

Teacher's Note:
1. Anecdotal records are open-ended, narrative and descriptive.
2. Do not confuse them with checklists, which only mark presence or absence of a behaviour.

Question 19: Which of the following is an example of a question with multiple answers?
(a) Given are the four digits 9, 3, 7, 5. Make the largest 4-digit number using all the given digits.
(b) Using four different digits without repetition, make the largest 4-digit number.
(c) Using four different digits, make the largest 4-digit number with a condition that 5 is always at units place.
(d) Make one 4-digit number using both the digits 3 and 5 equal number of times.
Show Answer & Explanation

Answer: (d) Make one 4-digit number using both the digits 3 and 5 equal number of times.

Explanation:
1. Options (a), (b) and (c) each have exactly one answer: 9753, 9876 and 9875 respectively.
2. In (d) each of 3 and 5 must appear twice, and the other arrangements such as 3355, 3535 and 5533 all work, so there are many answers.

Teacher's Note:
1. An open-ended question has more than one correct answer.
2. Check whether the conditions fix the answer completely.

Question 20: Four of your students made the following statements, after studying the concept of probability. Though no statement is fully correct, who is showing the MOST conceptual clarity?
(a) I don't know if it will rain tomorrow or not. So the probability of raining is 0.
(b) I am sure my favourite team will win tomorrow's match. So probability is not relevant here.
(c) Since petrol prices have been increasing for the last one year, probability of them increasing further is 100%.
(d) I don't know what scores I will get in the exam tomorrow. So probability of my passing the exam is 50%.
Show Answer & Explanation

Answer: (c) Since petrol prices have been increasing for the last one year, probability of them increasing further is 100%.

Explanation:
1. Statement (c) uses past data to estimate a probability, which is a reasonable idea, though 100% is too strong.
2. The others wrongly equate not knowing with probability 0 or 50%, or say probability is irrelevant when the outcome is uncertain.

Teacher's Note:
1. Probability measures how likely an uncertain event is, based on evidence.
2. The 50-50 fallacy (two outcomes, so equal chance) is a common misconception.

Question 21: According to National Curriculum Framework (2005), which of the following are considered to make mathematics learning more joyful and interesting?
(a) Using textbooks full of colours and pictures.
(b) Using mnemonic techniques to help students memorize formulae.
(c) Including puzzles, stories and mathematical tricks in everyday lessons.
(d) Using computer based resources extensively for teaching.
Show Answer & Explanation

Answer: (c) Including puzzles, stories and mathematical tricks in everyday lessons.

Explanation:
1. NCF 2005 suggests puzzles, games, stories and stimulating problems to make mathematics enjoyable.
2. Memorising and colourful books alone do not build interest in thinking.

Teacher's Note:
1. NCF 2005 wants mathematics to be a source of joy, not fear.
2. Look for options that involve thinking and play.

Question 22: According to National Curriculum Framework, 2005, one of the main aims of upper primary school mathematics teaching is to:
(a) help students understand that mathematics is a difficult subject
(b) inculcate discipline in the students
(c) help students develop mathematical thinking to handle abstractions
(d) prepare students for professional occupations in future
Show Answer & Explanation

Answer: (c) help students develop mathematical thinking to handle abstractions

Explanation:
1. NCF 2005 states the main goal of mathematics education is the mathematisation of the child's thinking.
2. At the upper primary stage this includes moving toward abstraction.

Teacher's Note:
1. The aim is thinking and problem solving, not just content.
2. Options calling mathematics difficult are always wrong.

Question 23: A mathematics teacher gave a statement in her class that in a triangle, the square of hypotenuse is equal to the sum of the square of other two sides. One of the students disagreed with this statement. Then teacher initiated the discussion in the class. Her aim is to:
(a) Encourage the shy students in the class to speak
(b) Pass the remaining time of the lecture
(c) Help students to realize that in mathematics there could be a disagreement
(d) See which students were more attentive in listening and responding in the class
Show Answer & Explanation

Answer: (c) Help students to realize that in mathematics there could be a disagreement

Explanation:
1. The statement is true only for right-angled triangles, so the student's disagreement has a valid basis.
2. Discussing it shows that mathematical claims can be questioned and must be justified.

Teacher's Note:
1. Mathematics grows through questioning, conjecture and justification.
2. Always check the conditions under which a theorem holds.

Question 24: Which of the following is NOT helpful in building the concept of place value in children?
(a) Abacus
(b) Geogebra
(c) Dienes Block
(d) Bundling of match sticks
Show Answer & Explanation

Answer: (b) Geogebra

Explanation:
1. Abacus, Dienes blocks and bundles of sticks are concrete materials that show ones, tens and hundreds.
2. GeoGebra is geometry software and is not a place-value tool.

Teacher's Note:
1. Place value is built with concrete grouping in tens.
2. GeoGebra is mainly for geometry and graphs.

Question 25: Abhishek is an elementary school mathematics teacher. He reads various books on mathematics to understand alternate concepts and misconceptions of children in mathematics. He focuses on various strategies to teach different topics in every class. Which of the following is least appropriate for Abhishek?
(a) He is preparing for an upcoming school inspection
(b) He is focusing on developing pedagogical-content-knowledge
(c) He is focusing on developing subject-matter knowledge
(d) He is focusing on learning new methods to solve textbook questions
Show Answer & Explanation

Answer: (a) He is preparing for an upcoming school inspection

Explanation:
1. Abhishek's reading and varied strategies show genuine professional growth in content and pedagogy.
2. Preparing for an inspection is a short-term motive and does not fit his regular practice.

Teacher's Note:
1. Pedagogical content knowledge combines subject knowledge with how to teach it.
2. Read the word 'least' carefully.

Question 26: The definition "Mathematics is a way to settle in the mind, a habit of reasoning" is given by _______ .
(a) Locke
(b) Galileo
(c) Bruner
(d) Napoleon
Show Answer & Explanation

Answer: (a) Locke

Explanation:
1. This definition is attributed to John Locke.
2. The other names are not associated with it.

Teacher's Note:
1. Remember definitions of mathematics with their authors, for example Locke, Galileo and Bacon.
2. Galileo called mathematics the language of nature.

Question 27: To find the value of exponential number operation like a × a etc., the teacher first writes all the formulae on the black board and then instructs the students to solve many examples based on the formulae. This is an example of:
(a) Inductive method of teaching
(b) Deductive method of teaching
(c) Scientific method of teaching
(d) Child centered method of teaching
Show Answer & Explanation

Answer: (b) Deductive method of teaching

Explanation:
1. Giving the general rule first and then applying it to examples goes from general to particular.
2. This is the deductive method.

Teacher's Note:
1. Inductive: examples first, then the rule. Deductive: rule first, then examples.
2. Deductive is quick but gives less discovery.

Question 28: Which of the following data sets cannot be represented using a pie chart?
(a) A record of change in temperature in a day
(b) Percentage of marks obtained by students in a class of 'n' number of students
(c) Ratio of number of students belonging to different states in a classroom
(d) Monthly expenditure of a family in various sectors
Show Answer & Explanation

Answer: (a) A record of change in temperature in a day

Explanation:
1. A pie chart shows parts of a whole.
2. Temperature changing through the day is not parts of a total, and a line graph suits it.

Teacher's Note:
1. Pie charts suit shares, ratios and percentages of a whole.
2. Changes over time suit line graphs.

Question 29: Which of the following is NOT a characteristic of mathematics lesson planning?
(a) It makes teaching systematic and well organised.
(b) It helps students to develop the habit of undertaking immediate corrective measures.
(c) It helps teacher in developing insights about learning needs and abilities of children.
(d) It helps teachers to learn to foresee and tackle learning difficulties of children.
Show Answer & Explanation

Answer: (b) It helps students to develop the habit of undertaking immediate corrective measures.

Explanation:
1. Lesson planning is a teacher's activity that organises teaching and anticipates difficulties.
2. Developing students' habits of corrective action is not a feature of the plan itself.

Teacher's Note:
1. A lesson plan serves the teacher's preparation.
2. Eliminate options that attribute the outcome to students.

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